Question

Write the first trigonometric function in terms of the second for θ in the given quadrant.
sec θ, sin θ; θ in Quadrant III
sec θ =

Answer 1

In quadrant I, both sec θ and sin θ are positive.
Thus, we do not need to do any sign changes.

sec θ
= 1 / cos θ
= 1 / sqrt(1 - sin^2 θ)

Note that sin^2 θ + cos^2 θ = 1